The representation of data
Machine Learning and Data Mining

Lecture outline 2
Components of the input
Concepts, instances, and attributes
Attributes types
Nominal
Ordinal
Interval
Ratio
Missing values and inaccurate values
Prof. Pier Luca Lanzi

Components of the input 3
Concepts
Kinds of things that can be learned
Instances
the individual, independent examples of a concept
Attributes
measuring aspects of an instance
Prof. Pier Luca Lanzi

What’s in an example? 4
Instance: specific type of example
Thing to be classified, associated, or clustered
Individual, independent example of target concept
Characterized by a predetermined set of attributes
Input to learning scheme: set of instances/dataset
Represented as a single relation/flat file
Rather restricted form of input
No relationships between objects
Most common form in practical data mining
Prof. Pier Luca Lanzi

What’s in an attribute? 5
Each instance is described by a fixed predefined
set of features, its “attributes”
But the number of attributes may vary in practice
Possible solution: “irrelevant value” flag
Related problem: existence of an attribute may depend of
value of another one
Possible attribute types (“levels of measurement”):
Nominal, ordinal, interval and ratio
Prof. Pier Luca Lanzi

The contact lenses data 6
Age Spectacle prescription Astigmatism Tear production rate Recommended
lenses
Young Myope No Reduced None
Young Myope No Normal Soft
Young Myope Yes Reduced None
Young Myope Yes Normal Hard
Young Hypermetrope No Reduced None
Young Hypermetrope No Normal Soft
Young Hypermetrope Yes Reduced None
Young Hypermetrope Yes Normal hard
Pre-presbyopic Myope No Reduced None
Pre-presbyopic Myope No Normal Soft
Pre-presbyopic Myope Yes Reduced None
Pre-presbyopic Myope Yes Normal Hard
Pre-presbyopic Hypermetrope No Reduced None
Pre-presbyopic Hypermetrope No Normal Soft
Pre-presbyopic Hypermetrope Yes Reduced None
Pre-presbyopic Hypermetrope Yes Normal None
Presbyopic Myope No Reduced None
Presbyopic Myope No Normal None
Presbyopic Myope Yes Reduced None
Presbyopic Myope Yes Normal Hard
Presbyopic Hypermetrope No Reduced None
Presbyopic Hypermetrope No Normal Soft
Presbyopic Hypermetrope Yes Reduced None
Presbyopic Hypermetrope Yes Normal None
Prof. Pier Luca Lanzi

The weather problem 7
Outlook Temperature Humidity Windy Play
Sunny Hot High False No
Sunny Hot High True No
Overcast Hot High False Yes
Rainy Mild Normal False Yes
… … … … …
Outlook Temperature Humidity Windy Play
Sunny 85 85 False No
Sunny 80 90 True No
Overcast 83 86 False Yes
Rainy 75 80 False Yes
… … … … …
Prof. Pier Luca Lanzi

Nominal quantities 8
Values are distinct symbols
Values themselves serve only as labels or names
Example
Attribute “outlook” from weather data
Values: “sunny”,”overcast”, and “rainy”
No relation is implied among nominal values
No ordering
No distance measure
Only equality tests can be performed
Prof. Pier Luca Lanzi

Ordinal quantities 9
Impose order on values
No distance between values defined
Example:
The attribute “temperature” in weather data
Values: “hot” > “mild” > “cool”
Addition and subtraction don’t make sense
Example rule:
temperature < hot Þ play = yes
Distinction between nominal and ordinal not always clear
(e.g. attribute “outlook”)
Prof. Pier Luca Lanzi

Interval quantities 10
Interval quantities are not only ordered but measured in
fixed and equal units
Examples
Attribute “temperature” expressed in degrees
Attribute “year”
Difference of two values makes sense
Sum or product doesn’t make sense
Zero point is not defined
Prof. Pier Luca Lanzi

Ratio quantities 11
Ratio quantities are ones for which the
measurement scheme defines a zero point
Example
Attribute “distance”
Distance between an object and itself is zero
Ratio quantities are treated as real numbers
All mathematical operations are allowed
Is there an “inherently” defined zero point?
It depends on scientific knowledge
E.g. Fahrenheit knew no lower limit to temperature
Prof. Pier Luca Lanzi

Attribute types used in practice 12
Most schemes accommodate just two levels of
measurement: nominal and ordinal
Nominal attributes are also called “categorical”,
”enumerated”, or “discrete”
But: “enumerated” and “discrete” imply order
Special case: dichotomy (“boolean” attribute)
Ordinal attributes are called “numeric”, or “continuous”
But: “continuous” implies mathematical continuity
Prof. Pier Luca Lanzi

Why specify attribute types? 13
Why Machine Learning algorithms need
to know about attribute type?
To be able to make right comparisons and
learn correct concepts
Example
Outlook > “sunny” does not make sense, while
Temperature > “cool” or
Humidity > 70 does
Additional uses of attribute type
Check for valid values
Deal with missing, etc.
Prof. Pier Luca Lanzi

Nominal vs. ordinal 14
Attribute “age” nominal
If age = young and astigmatic = no
and tear production rate = normal
then recommendation = soft
If age = pre-presbyopic and astigmatic = no
and tear production rate = normal
then recommendation = soft
Attribute “age” ordinal
(e.g. “young” < “pre-presbyopic” < “presbyopic”)
If age≤pre-presbyopic and astigmatic = no
and tear production rate = normal
then recommendation = soft
Prof. Pier Luca Lanzi

Missing values 15
Frequently indicated by out-of-range entries
Types: unknown, unrecorded, irrelevant
Reasons:
Malfunctioning equipment
Changes in experimental design
Collation of different datasets
Measurement not possible
Missing value may have significance in itself
E.g. missing test in a medical examination
Most schemes assume that is not the case
“missing” may need to be coded as additional value
Does absence of value have some significance?
If it does, “missing” is a separate value
If it does not, “missing” must be treated in a special way
Prof. Pier Luca Lanzi

Inaccurate values 16
What is the reason?
data has not been collected for mining it
What is the result?
errors and omissions that don’t affect original purpose of
data (e.g. age of customer)
Typographical errors in nominal attributes,
thus values need to be checked for consistency
Typographical and measurement errors in numeric
attributes, thus outliers need to be identified
Errors may be deliberate (e.g. wrong zip codes)
Other problems: duplicates, stale data
Prof. Pier Luca Lanzi

Getting to know the data 17
Simple visualization tools are very useful
Nominal attributes: histograms
Numeric attributes: graphs
2-D and 3-D plots show dependencies
Need to consult domain experts
When there is too much data to inspect, take a sample!
Prof. Pier Luca Lanzi